A069535 Treated as strings, n and its reversal are substrings of n!.

1, 2, 4, 20, 30, 33, 42, 44, 45, 51, 60, 67, 72, 75, 78, 79, 80, 81, 82, 84, 88, 91, 94, 95, 97, 98, 99, 116, 140, 141, 166, 170, 180, 188, 198, 200, 202, 210, 222, 228, 231, 238, 252, 261, 264, 265, 272, 285, 286, 292, 293, 297, 311, 313, 315, 317, 321

Offset: 1

Author

Joseph L. Pe, Apr 16 2002

Keywords

• base
• nonn

Comments

This is the sequence of "fixated points" (cf. A068588) of f(n) = n!.

Examples

			42! = 1405006117752879898543142606244511569936384000000000, which contains both 42 and 24 as substrings. Hence 42 is a term of the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Pe, J. Fixated Points of Arithmetical Functions

Crossrefs

Cf. A068588.

Programs

Maple

filter:= proc(n) local m,L,R,LN; uses StringTools;
  L:= sprintf("%d",n);
  m:= padic:-ordp(n,10);
  R:= Reverse(L)[m+1..-1];
  LN:= sprintf("%d",n!);
  Search(L,LN) > 0 and Search(R,LN) > 0
end proc:
select(filter, [$1..1000]); # Robert Israel, Apr 28 2021

Mathematica

r = {}; Do[m = n!; s = ToString[m]; If[ StringPosition[s, ToString[n]] != {} && StringPosition[s, ToString[ FromDigits[ Reverse[ IntegerDigits[n]]]]] != {}, r = Append[r, n]], {n, 1, 321}]; r

Extensions

Edited and extended by Robert G. Wilson v, Apr 19 2002